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Use the formula for \((a+b)^2=a^2+2ab+b^2.\) Since \(2^8+2^{11}=(2^4)^2+2*2^4*2^6\), we need an extra term, that of \((2^6)^2=2^{12}\) to complete the expression to a perfect square, \((2^4+2^6)^2.\)

So, \(n\) should be \(12\).
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PhD in Applied Mathematics Love GMAT Quant questions and running.

Use the formula for \((a+b)^2=a^2+2ab+b^2.\) Since \(2^8+2^{11}=(2^4)^2+2*2^4*2^6\), we need an extra term, that of \((2^6)^2=2^{12}\) to complete the expression to a perfect square, \((2^4+2^6)^2.\)

So, \(n\) should be \(12\).

Thank you eva I think this approach is more justified, like it better
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